License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.65
URN: urn:nbn:de:0030-drops-124725
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12472/
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Hirai, Hiroshi ; Ikeda, Motoki

Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity

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LIPIcs-ICALP-2020-65.pdf (0.6 MB)


Abstract

The terminal backup problems [Anshelevich and Karagiozova, 2011] form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum cost subgraph satisfying the connectivity requirement. The node-connectivity terminal backup problem requires a terminal to connect other terminals with a number of node-disjoint paths. This problem is not known whether is NP-hard or tractable. Fukunaga (2016) gave a 4/3-approximation algorithm based on LP-rounding scheme using a general LP-solver. In this paper, we develop a combinatorial algorithm for the relaxed LP to find a half-integral optimal solution in O(mlog (mUA)⋅ MF(kn,m+k²n)) time, where m is the number of edges, k is the number of terminals, A is the maximum edge-cost, U is the maximum edge-capacity, and MF(n',m') is the time complexity of a max-flow algorithm in a network with n' nodes and m' edges. The algorithm implies that the 4/3-approximation algorithm for the node-connectivity terminal backup problem is also efficiently implemented. For the design of algorithm, we explore a connection between the node-connectivity terminal backup problem and a new type of a multiflow, called a separately-capacitated multiflow. We show a min-max theorem which extends Lovász - Cherkassky theorem to the node-capacity setting. Our results build on discrete convex analysis for the node-connectivity terminal backup problem.

BibTeX - Entry

@InProceedings{hirai_et_al:LIPIcs:2020:12472,
  author =	{Hiroshi Hirai and Motoki Ikeda},
  title =	{{Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{65:1--65:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12472},
  URN =		{urn:nbn:de:0030-drops-124725},
  doi =		{10.4230/LIPIcs.ICALP.2020.65},
  annote =	{Keywords: terminal backup problem, node-connectivity, separately-capacitated multiflow, discrete convex analysis}
}

Keywords: terminal backup problem, node-connectivity, separately-capacitated multiflow, discrete convex analysis
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020


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